Brachiation is the process of branching out, process of putting forth arms but it is associated with locomotion or swinging from tree to tree, and not the action of opening, or to open arms: an eager or warm welcome (New Collegiate Dictionary. 2001.)
I found one use for the action of "opening their arms wide to offer a hug" under the word 'open' listed as:
Spread ; expanded. He received his son with open arms -An American
dictionary of the English language; ... . Webster, Noah, 1758-1843.
but I suspect there may be a derivation from the many synonyms for the word 'hug', or the desire to do the action:
Clip: To hug or embrace -A classical dictionary of the vulgar tongue. . Grose, Francis, 1731?-1791.
Halch: To hug
Cingulomania: In a male, a strong desire to hold a girl in one's arms. A term possibly coined by J.E. Schmidt for the Lecher's Lexicon (1967).